E115PS1solutions - Problem Set 1 E115 - Thermodynamics -...

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Unformatted text preview: Problem Set 1 E115 - Thermodynamics - Fall 2011 Due: xx/yy 1. For the following list of systems, determine if each is open, closed, or isolated. You may choose to provide justification for your answer if you feel it is necessary (7 pts). For this problem, full credit is given if you gave the most appropriate answer, or if you provided an alternative answer with a reasonable explanation for your choice. A few examples of reasonable alternative answers are given in parenthesis. a) A pot of boiling water. OPEN - This is a classic open system. Heat comes in, water vapor goes out. (Calling it a closed system is only justifiable if you say that there is an extremely tight lid on this pot and that no gas escapes at all. However, most pot lids have an escape pathway to prevent pressurizing the pot) b) An ice pack. CLOSED - Heat flows out of the system when using it or into the system when re-freezing it, but it is sealed, and no material enters or leaves. c) A piece of steel. CLOSED - It can be heated or cooled, but no matter can leave without destroying the system itself. (However, one might consider a piece of steel slowly rusting over a long peroid of time, in which case its mass and composition is changing, and it is better described as open.) d) You. OPEN - This system constantly radiates heat and mass periodically flows across its boundaries. e) The Earth. CLOSED- Typically, only heat flows across the boundaries, in from the sun and out through the blackbody spectrum. (You could argue, however, that some very small percentage of its mass will occasionally enter or leave via asteriods, the space program, etc.) f) An internal combustion engine. OPEN - Uncombusted gas comes in, heat and combustion products leave. g) The entire universe. ISOLATED - There is nowhere else for heat or matter to go. 2. Consider an ideal gas in a spherical balloon. For this particular balloon, the internal pressure of the gas is related to the balloon radius, r , by the expression P = 1 + r 2 (1) where = 0 . 25 atm / cm 2 . (9 pts) a) The balloon is initially inflated to a radius of 6 cm at room temperature (22 C). How many moles of gas does the balloon contain? The first step in this problem is to set up the ideal gas law. n = PV RT We immediately notice that neither the pressure nor volume of the balloon are given. Fortunately, we can calculate both from the balloon radius. P = 1 + r 2 V = 4 3 r 3 Now we plug in the given values to find the number of moles in terms of radius, n = (1 + r 2 )(4 / 3 r 3 ) RT We can avoid unit conversions by choosing R in the given units, R = 82 . 05 atm cm 3 / molK, which gives n = 0 . 176 mol 1 b) You decide to make the balloon larger. If you have a lung capacity of 4 L, how many breaths should you add to the balloon to inflate it to a radius of 8 cm? You may assume that the air in your lungs remains at roomto the balloon to inflate it to a radius of 8 cm?...
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This note was uploaded on 09/23/2011 for the course ENGINEERIN 115 taught by Professor Hosemann during the Fall '11 term at University of California, Berkeley.

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E115PS1solutions - Problem Set 1 E115 - Thermodynamics -...

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